
where \(t\)  is the electron hopping constant, \(\mu \)  is the chemical potential of the electrons used to control the density of the doped holes, \(K\)  stands for the Kitaev interaction, \(\Gamma \)  and \(\Gamma ^{\prime }\)  are off-diagonal interactions. In later discussions, we assume \(K<0, \Gamma >0\)[1]}, [2]}, [3]}, [4]}, [5]}, and fix \(\Gamma ^{\prime }=-0.02|K|\)  (the \(\Gamma ^{\prime }\)  interaction is introduced to stabilize the zigzag order observed in Kitaev materials[6]}, [7]}).
